\documentclass{article}
\usepackage{amsmath}
\author{William Labbett}
\title{title}
\begin{document}
\maketitle
\tableofcontents
% REMS
% Must leave interest and things to do for the reader (Is that Delusional of me to think I might not?}
% How to put greek letter pi in text
% explain Real
\newpage
\section{Prerequisite Terms for Understanding This Document}
\begin{itemize}
\item WHOLE NUMBER
\item PROPER FRACTION
\item REAL NUMBER
\item $\lbrack x \rbrack$
\end{itemize}
\subsection{WHOLE NUMBER}
A WHOLE NUMBER is a number like 0, 1, 2, 3, 10, 308, \ldots
i.e the numbers used for counting.
\end{WHOLE NUMBER}
\subsection{REAL NUMBER}
A PROPER FRACTION is a fraction whose numerator which musn't be zero
is less than the denominator. e.g $\frac{4}{11}$
\end{REAL NUMBER}
\newpage
\section{Finding the Decimal Representation of Powers of Real Numbers}
When going about finding the decimal representation of the square
of a real number like $\pi$ it is helpful to express the number as
a sum of a WHOLE NUMBER and a real number from 0 to 1 i.e on the set (0,1).
Suppose we have a number X. If X = n + x where n is the whole
part of X and x is the number on the set (0,1) then
\begin{equation*}
X^2 = (n + x)^2 = n^2 + 2nx + x^2
\end{equation*}
To calculate $2nx$ to some specific number of decimal places is straightforward.
Calculating $x^2$ to a specified number of decimal places is more involved.
For an example, let X = 6.873416873640587613458072364......
In this case we have n = 6 and x = 0.873468736405876......
The meaning of 0.873468736405876 is \newline
\begin{equation*}
\frac{8}{10^1}+\frac{7}{10^2}+\frac{3}{10^3}+\frac{4}{10^4}+\frac{6}{10^5}
\end{equation*}
\end{document}